Discrete Mathematics, Algorithms and Applications, Volume (5), No (4), Year (2013-6) , Pages (135003501-135003512)

Title : ( Total graphs of Polynomial Rings and Rings of fractions )

Authors: مژگان افخمی گلی , Kazem Khashyarmanesh ,

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Let R be a commutative ring. The total graph of R, denoted by T(Γ(R)), is a graph with all elements of R as vertices, and two distinct vertices x, y ∈ R are adjacent if and only if x + y ∈ Z(R), where Z(R) denotes the set of zero-divisors of R. In this paper, we examine the preservation of the diameter, girth and completeness of T(Γ(R)) under extension to polynomial rings and rings of fractions. We also study the chromatic index, clique number and independence number of T(Γ(R)).

Keywords

Total graph; diameter; girth; polynomial rings; rings of fractions; chromatic index; clique
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@article{paperid:1039762,
author = {مژگان افخمی گلی and Khashyarmanesh, Kazem},
title = {Total graphs of Polynomial Rings and Rings of fractions},
journal = {Discrete Mathematics, Algorithms and Applications},
year = {2013},
volume = {5},
number = {4},
month = {June},
issn = {1793-8309},
pages = {135003501--135003512},
numpages = {11},
keywords = {Total graph; diameter; girth; polynomial rings; rings of fractions; chromatic index; clique number},
}

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%0 Journal Article
%T Total graphs of Polynomial Rings and Rings of fractions
%A مژگان افخمی گلی
%A Khashyarmanesh, Kazem
%J Discrete Mathematics, Algorithms and Applications
%@ 1793-8309
%D 2013

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